Pathways to mathematical excellence: An international perspective

Nancy Lee Long

Abstract

This study examines paths students have constructed to mathematical excellence; it consists of two foci and is the joint pursuit of two researchers. The first focus is national and seeks solutions to the problem of the highly capable youth who experiences perpetual boredom in his math classes. Many available flexible options are defined and discussed. They include acceleration, AP courses, dual enrollment, fast-paced residential schools, early college entrance, special summer programs, math competitions, and mentoring. Solving the boredom problem sometimes causes undue pressure on the math student, so burnout is also addressed. The second focus is international and seeks to consider how the American mathematical fingerprint compares with that of our genetic parent--England. The researcher chose Oxford, with its long history and consistency in retaining its academic traditions, and compared the Oxford tradition to Princeton, frequently rated as having the top American undergraduate program in mathematics. Eleven math majors in their third and fourth year at each school answered a short answer and free response survey, the focus of which was different than the national survey. The Oxford - Princeton survey sought differences in curriculum, methodology, and assessment for consideration. An internet interview was conducted with a Princeton student who had studied abroad at Oxford for a year. Analysis of the survey results showed that Princeton students, compared with their Oxford counterparts, spent a smaller percentage of their course load in mathematics classes; were more likely to have been active participants in math competitions; preferred to be tested on a more frequent basis; and were less likely to have developed a beneficial relationship with a teacher or mentor. The Princeton and Oxford students were alike in many ways. They were taught mathematics primarily by lectures with small reliance on computers or calculators; were likely to have been strongly attracted to math at a very early age and to remain quite passionate in its pursuit; were equally likely to have experienced boredom or burnout; and were equally likely to have taught themselves a math topic. Reflections from a Princeton/Oxford student provided additional valuable comparative information and affective judgement.